On 2-powerfully Perfect Numbers in Three Quadratic Rings

2014/12/09 by Colin Defant, Defant, Colin · 2 citations
Mathematics · Physics and Astronomy · #11N80 #11R11 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N80 #msc:11R11

paper · pdf · doi:10.48550/arxiv.1412.3072

15 pages, 0 figures, Supported by National Science Foundation grant no. 1262930

openalex publication_date 2014/12/09 · arxiv created 2014/12/11 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call n-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that have been defined and studied in the integers. We investigate the properties of 2-powerfully perfect numbers in the rings \mathcal O_ℚ(√(-1)), \mathcal O_ℚ(√(-2)), and \mathcal O_ℚ(√(-7)), the three imaginary quadratic rings with unique factorization in which 2 is not a prime.

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• Multiperfect Numbers in Certain Quadratic Rings

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